# Calculating independent rates when the assumption is neither UDD nor CFM

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asked Nov 23, 2017

This question pertains to the following past test question.

4. Consider a three-decrement model of which it may be assumed that decrements 1 and 2 are distributed uniformly in their respective single-decrement tables, but that decrement 3 is concentrated at the end of the year of age.

How do we work with the 3rd decrement? We obviously wouldn't use our formulae as normal. Or would we?

I am struggling to get to an intuitive method of working out the dependent rates given that only two of the independent rates are uniformly distributed.

## 1 Answer

+1 vote
answered Nov 24, 2017 by (2,950 points)

You would calculate the dependent rates of the two UDD ones as per normal (as if there were just 2 decrements) - they 'take place' before the one at the end. After reducing the in-force lives by the first 2 UDD decrements, then apply the one concentrated at the end to the remaining lives.

The number of lives exiting due to this decrement at the end divided by the number in force at the start of the period (before the other two decrements) will be the dependent rate.

Conversely, similar logic holds for decrements at the start that apply before the other decrements.

You are correct that you treat it differently, but the rest as per normal, and then just apply the concentrated decrement in the right order, first or last.